Thursday, May 31, 2012

It's well known that 'queer theorists' successfully reclaimed the term 'queer', which used to be a term of abuse for homosexual, and turned it into a sort of verbal flag for the homosexualist movement.

Can we do the same thing for the term 'prude'? By far the most common statement I see on one side of the porn debate is 'I am not a prude' (the most common statement on the other side is 'I am against any form of censorship'). But I am always puzzled by what a 'prude' is. It seems like a term of abuse, given that so many people are so eager to deny being one. I have never seen anyone admit to being a prude. Is this because prudes are a bit like homosexuals were in the 1950s, and afraid to admit this. Should prudes come out of the closet? It's difficult to say, because whereas it was clear in the 1950s what 'homosexual' meant, it's not clear what 'prude' means.

So we can't reclaim a term if we don't know what it means. Time for some further research.

Maverick has just posted a reply to my request for what he calls a ‘sound bite’ on his argument for circularity. Before I comment, a brief aside on my dislike of the term ‘sound bite’. In philosophy, particularly ‘Internet philosophy’, I frequently encounter it when I ask for a clear and concise explanation of or argument for the opponent’s position. “You can’t reduce my argument to a sound bite”. Well in that case I am not interested in the opponent’s argument, for it is not an argument at all. I suspect the underlying reason is a fear that the position really is incoherent, or that the underlying argument is invalid. There should be an informal fallacy ‘The Sound Bite fallacy’ named after it. And in any case I do not want a ‘sound bite’, which is simply a short slogan summarising a position or attitude such as ‘This was their finest hour’, often little more than a cliché. Note also my previous post, where I argued that the ‘circularity objection’ is actually more complex and difficult than Maverick originally implied, and that it is unfair to say I am being disingenuous, when I claim I fail to understand it. I feel he has now conceded that it is somewhat more complicated and less obvious than he originally suggested.

But anyway: Maverick has now given a pretty clear outline of his argument, which I copy verbatim below.

1. On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated.'
2. If a first-level concept such as *F* is instantiated, then it is instantiated by an individual.
3. Let the arbitrary constant 'a' denote an individual that instantiates *F.*
4. By LNC, a cannot both exist and not exist.
5. By LEM, a must either exist or not exist.
6. If a does not exist, i.e., if a is a Meinongian nonexistent object, then the link expressed in (1) between existence and instantiation is broken.
Therefore
7. If *F* is instantiated, then *F* is instantiated by an individual that exists.
Therefore
8. On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated by an individual that exists.'
9. A definition (analysis, account, theory, explanation) is circular iff the term to be defined occurs in the defining term.
10. 'Exists' occurs both in (8)'s definiendum and its definiens.
Therefore
11. The thin theory is circular.

Is it valid? Well, my first point is that the argument is even more complex than this, by reason of premisses (7) to (10). Consider the following, obviously invalid argument:

(1a) ‘Bachelor’ means the same as ‘unmarried man’.
(2a) (From 1a, definition) Every bachelor is an unmarried man.
(3a) Every bachelor is a bachelor who is an unmarried man.
(4a) ‘Bachelor’ means the same as ‘bachelor who is an unmarried man’.
(5a) ‘Bachelor’ occurs in the definiendum and the definiens of (4a)
(6a) The definition of ‘bachelor’ is circular.

What’s wrong with it? Well, from the fact that a definition occurs somewhere in the argument it doesn’t follow that whatever we derive from the definition can itself be turned into a definition. The universal proposition (3a) above is perfectly true and follows from the original definition, but it doesn’t follow that we can turn any old universal proposition into a definition. So the move to (4a), which turns the universal proposition into a definition, is blatantly fallacious.

Likewise, even if I grant the truth of the universal proposition corresponding to Maverick’s (7) above, i.e. “any F that exists is an F instantiated by an individual that exists”, it doesn’t follow that you can turn this into something that looks like a definition. Quite obviously not. In particular, Bill needs to avoid the charge that he has reintroduced the term ‘exist’ in (7) in much the same way that ‘bachelor’ has been reintroduced in (3a).

By Larry Sanger here. The logic of arguments for and against porn is interesting, although I don't have a great deal of time to go into it now. The top level argument, as it were, is that people, i.e. all people, should have the right to see absolutely whatever they like, and that any restriction is an encroachment upon freedom. The objection to this is that not all people, namely young children, should have this right. Then we encounter all sorts of counter-objections and replies to the counter-objections. For example, what exactly is wrong with children seeing such images. If sex good or not? If it is good, why shouldn't children participate in the good, etc etc. Larry (who is a philosopher) covers some of these arguments in his post.

At least Augustine had a clear approach to this. Sex, or rather shame about sex, is the result of original sin. I'll look up the reference some time.

Wednesday, May 30, 2012

"It ain't obvious what's obvious". Thanks to the Maverick for that insight by Hilary Putnam. I suppose everyone knows the mathematician's joke about the lecturer how - discussing some result - says 'That's obvious'. He then pauses, looks down, then goes off for about twenty minutes. Then he comes back and announces 'Yes, it's obvious'.

Judging from the comments, there's been a bit of misunderstanding about my position on the 'thin conception' of existence. I don't necessarily agree with the conception. My question is whether the brief arguments given by Maverick, and which seem as obvious as day to him, really are obvious. Now I think, pace Dr. Putnam, there is a simple test for obviousness. If you can state your position or argument in less than about five sentences, and if the terms are clear or well-defined, or have a common and undisputed meaning, if any assumptions underlying the position are beyond dispute, and if all deductive steps are valid, then it is obvious. Otherwise it isn't.

Now Maverick's argument, as I understand it, is this:

The thin conception of 'exists' is that 'An F exists' means the same as 'The concept *F* is instantiated'
But if *F* is instantiated, then it is instantiated by an individual that exists
Therefore the thin conception of 'exists' is circular

This is deceptively simple, but fails my test for obviousness. Why? The subject of the conclusion is 'the thin conception of exists'. The predicate is 'circular'. The predicate of the conclusion is called the 'major term' and it is an undisputed rule of logic that the major term should appear in the premisses. Which of course it doesn't. This would probably be fine if the idea of a circularity were undisputed and clear, by I have argued elsewhere that it isn't. It is very slippery.

So what is needed is an argument of the following form:

The thin conception of existence is of form X
Any conception of form X is circular
The thin conception of existence is circular.

I would accept any argument of that form as 'obvious'. And I hope that clears me of any charges of being disingenuous.

Tuesday, May 29, 2012

There is a further installment from the Maverick in the dispute about the thin conception of existence. Maverick asks whether I think the notion of a non-existent object is self-contradictory. I reply: we need to be shown that it is self-contradictory. The thin conception of existence is first and foremost a definition, and you can't argue against a definition as such. The only way of progressing is to show how the defined term in its ordinary (or perhaps philosophical) use is not consisent with the definition. But I am not seeing that in any of Maverick's arguments, and particularly the 'circularity' argument, which I entirely fail to understand.

One of his arguments, for example, is that there is an inbuilt assumption that the domain of quantification contains only existing things. But in what sense is he using the italicised 'existing' here? If in the sense that the Brentano defines it, then the domain does contain only existing things, but in the most trivial and non-circular way, for the word 'thing', by definition, means 'existing thing' or 'thing which is a thing'. If in some stronger sense, Maverick needs to explain what that sense is. Those of us trained in the analytic method are taught to give examples. Find a use of the verb 'exists' that is not consistent with the definition set out by Brentano. But I am not seeing that.

Maverick ends:

Ed begs the question against me by simply stipulating that the meaning of the verb 'exists' shall be identical to the meaning of 'Some ___ is a --.' That is what I deny.

Not at all. I am questioning his arguments to show that 'exists' has any meaning stronger than that. I would like to see an argument with numbered steps, with assumptions clearly labelled, with any deductive steps clearly identified. All I am seeing is European 'novelistic' gestures at an argument, with laboured repetition of the same point, and without logical justification of that point. Like CJFW, who I mentioned in an earlier post, I don't do Continental.

I just noticed the Maverick’s comment on C.J.F. William’s obituary here, and was struck by the fact that his wheelchair-bound existence was news. This reminded me of the contrast between what we know of the thought of a philosopher such as Duns Scotus, which is immense, and what we know of his life, which is almost nothing, and what we do know is mostly guesswork based on other facts, and thus is not even knowledge.

CJF being in a wheelchair was in one way the most striking thing about him. I remember helping carrying it – with him in it – up the steps of the Wills building. The building was designed in the grand neo-Gothic manner (in about 1908) and so the flight of steps was about half a mile long, and I remember entertaining with horror the idea of us letting go the wheelchair and it moving with gathering speed to the bottom where it would crash into the porter’s lodge with horrifying consequences, perhaps carrying off a few undergraduates along the way.

But in another way it was the least important, and once you got to know him, you were hardly ever aware of it. He was teaching philosophy after all.

One story he liked to tell was about his special trousers he had, with a zip at the back going right up from bottom to top. A colleague came to collect him one day, and saw a spare pair of these lying on the floor, fully unzipped and looking like a tiger skin rug, except without the stripes. “Now I understand the difference between appearance and reality”, said the colleague.

There was a constant philosophical war going on between CJF and another philosopher in the department, Edo Pivcevic. Edo was Czech, or from some central European place – he was hired by the late Stefan Korner – and was a ‘phenomenologist’ always talking about Husserl and Heidegger, and saying things like ‘to answer the question about the meaning of being we must analyse the being of Man’. CJF was utterly contemptuous of this European stuff, although he taught Frege and Wittgenstein, who were very European in their own way.

CJF also told a Swinburne story. Once Swinburne offered to drive him from some place to another, probably Bristol to Manchester. However, Swinburne qualified the offer by saying he never drove over 30 miles an hour. Thinking he meant urban zones where a 30 mph limit applies in Britain, and thinking this exemplary practice, he accepted. What Swinburne meant, however, was that he drove at this speed even on motorways, where most people are whizzing along at speeds in excess of 70 mph. I don’t know how long it took to get to Manchester up the M5, although I can picture it.

Monday, May 28, 2012

David Brightly on singular existential statements here. I liked this bit

[...] there is an important asymmetry between singular existential assertions and denials. If the name 'Vulcan' has been properly introduced by a general existential assertion then 'Vulcan exists' tells us nothing new. In contrast, 'Vulcan doesn't exist' amounts to a denial of the general existential statement by which the name was introduced to us. On the other hand, if the name 'Vulcan' has not been properly introduced then 'Vulcan exists' is meaningless to us.

Ed thinks that the assumption that the domain of quantification is a domain of existing individuals is a contingent assumption. But I didn't say that, and it is not. It is a necessary assumption if (1) [namely that ‘Island volcanos exist’ is logically equivalent to ‘Some volcano is an island.’] and sentences of the same form are to hold. [My emphasis]

But he then says that there is nothing in the nature of logic to stop us from quantifying over nonexistent individuals, which I don't follow at all. We start with the initial logical or definition assumption about the meaning of the verb 'exists'.

(1) 'A golden mountain exists' = 'Some mountain is golden'

If we accept that, we also have to accept the equivalence where the right hand side does not explicitly contain the copula 'is', but has a verb which is logically equivalent to a copula plus participle. That is a standard assumption, namely that 'John runs' is logically equivalent to 'John is running'. Thus

(2a) 'John owns a house' = 'some house is owned by John

and thus, given (1), and given that John owns a house, it follows that:

(2b) John's house exists

A brief qualification here. The equivalence in (2a) only holds when the verb is what I call 'logically transitive. I explain this idea here. Clearly, if John wants a beautiful wife, it does not follow that some beautiful wife is wanted by John. Given that, it is plain that our Brentano equivalence applies to the following quantifier type sentences:

(3) 'The domain contains islands' = 'some individuals in the domain are islands' = 'there exist individuals in the domain which are islands'

and so on. Hence there clearly is something 'in the nature of logic' which prevents us quantifying over non-existent individuals, namely the same thing as what prevents us owning non-existent houses, given the definition of 'exists' above. I can't believe that Bill does not grasp this. I think what he fails to see is that 'logical' verb phrases like 'ranges over', 'contains', 'quantifies over' are subject to the same logical rules as 'owns', 'lives next door to', 'loves' and so on. That any domain contains existing individuals is therefore a logical truth.

Sunday, May 27, 2012

I mentioned Frege's distinction between concept and object earlier, and said I was taking a feature of that distinction as fundamental, namely that the distinction between predicate and sentential negation only applies to concept words (or rather, quantified concept words), and not to object words ('logical subjects').

David Brightly wasn't so sure it was a feature of that distinction, as opposed to a mere accident. Well, two further reasons. First, it is build into the predicate calculus that simple singular propositions have only one form of negation. We write '~Fa'. The syntax of the calculus is designed so that we cannot even represent the difference between 'Socrates is not running' and 'it is not the case that Socrates is running'.

Second, Frege begins his discourse by saying that a concept is predicative, whereas the name of an object, a proper name, is quite incapable of being used as a grammatical predicate. Now, we can say that someone is Alexander the Great, or is the planet Venus, but this is not predicating the object itself. For the predicate 'is the planet Venus' is predication not of Venus itself but of the concept of being identical with Venus. The verb 'is' is not a mere copula, its content is an essential part of the predicate.

Thus for an object-word to signify, it has to signify an object. It is essential to an object word like 'Venus' that it has to be satisfied, whereas it is essential to a concept word like 'planet' that it can be satisfied, or not. "An equation is reversible; an object's falling under a concept is an irreversible relation.

Thus "‘Venus exists’ is true in virtue of the meaning of the proper name ‘Venus’. Maverick says that this has it precisely backwards. What I should say is that 'Venus' has meaning in virtue of the truth of 'Venus exists'. Not at all. 'Venus' has meaning in virtue of its meaning something, just as you are an employer in virtue of your employing someone.

Saturday, May 26, 2012

Maverick finally replies to my circularity objections. I agree with his broad conclusion, as it happens. I just disagree with his way of getting there. He argues (I have numbered his sentences).

1. ‘Island volcanos exist’ is logically equivalent to ‘Some volcano is an island.’

Agree, of course.

2. This equivalence, however, rests on the assumption that the domain of quantification is a domain of existing individuals.

Disagree profoundly. The equivalence, being logical, cannot depend on any contingent assumption. From the logical equivalence of (1), it follows that ‘the domain of quantification is a domain of existing individuals’ is equivalent to ‘some individuals are in the domain’. But the equivalence is true whether or not any individuals are in the domain. E.g. suppose that no islands are volcanoes. Then ‘Some volcano is an island’ is false. And so is ‘island volcanos exist’, by reason of the equivalence. But the equivalence stands, because it is a definition. Thus the move from (1) to (2) is a blatant non sequitur.

3. If the domain were populated by Meinongian nonexistent objects, then the equivalence would fail.

This rests on the assumption that it is a contingent matter whether the description ‘Meinongian nonexistent objects’ is satisfied. But if the equivalence is logical, i.e. if ‘some objects are in the domain’ is logically equivalent to ‘some object in the domain exists’, then by definition there cannot be Meinongian nonexistent objects, any more than there can be bachelors who are married. Maverick takes an equivalence which is purportedly true by definition, then turns it into a contingent statement. But if it is contingent, the equivalence cannot be true by definition, he argues, and the rabbit is out of the hat.

4. The attempted reduction of existence to someness is therefore circular.

Wrong. The argument is fallacious, because the move from (1) to (2) is fallacious. We cannot agree that something is true by definition, i.e. subject and predicate are logically equivalent, to making its truth a contingent matter, as in (2).

Jon Davies (Chief Executive of Wikimedia UK) gave me a 'Schools Wikipedia' CD which I gratefully accepted along with a Wikimedia UK coffee mug, which I use for my early morning mug (thank you Jon!).

I didn't look at the disc until today, fearing what horrors there might be, but actually it is quite good. It has clearly been edited to remove the worst of the grammatical abominations. The pictures are a more sensible size so there is none of that ugly white space, and, best of all, no footnotes except where necessary. The links to the very worst article have been removed.

Yet there is one more thing of great significance. When I checked the Age of Enlightenment article, it was much better than the version of the article I criticised here. For example, I criticised the current article (permalink) as stating that the Age of Enlightenment was a movement when, as its name suggests, it is a period. The schools article, by contrast, correctly states that it is a period after all.

Sigh of relief that the corruption of our schoolchildren is not imminent, at least in this case. But why the difference? Had the mistakes been edited out by professionals? Well, probably not. A bit of research shows that the school version dates from around October 2005. Which bears out what I have always said. A lot of reasonably good people were contributing to Wikipedia around that time, then left after a wave of vandalism and trolling hit the project in 2006. The vandalism was like 'drinking water from a firehose'. This was countered by a massive increase in the number of vandal fighters, but at the same time and by that very token the project was turning from building into an encyclopedia, which requires certain skills, to protecting against vandals, as well as running a secret intelligence force that would have made Stalin proud, and this requires different skills.

Very significant that the quality of Wikipedia has got demonstrably worse over 2005-12.

Friday, May 25, 2012

Here I mentioned Frege's distinction between concept and object, and Anthony is rightly asking questions about it. How does direct reference relate to the distinction?

So I go back to Frege, and his famous essay. It's rather hard to get anything out of it, because he never properly defines the distinction. He says that his explanation is not meant as a proper definition. "One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance". What is logically simple cannot have a proper definition (as Aristotle also noticed).

But he does give the famous example of "all mammals are land dwellers", which will do for my purpose. He says that if 'all mammals' were the logical subject of 'are land dwellers', then to negate the whole sentence we should have to negate the predicate, giving "all mammals are not land-dwellers". That is obviously wrong, for this predicate negation gives the contrary of the sentence it negates, not the contradictory. Thus we must put the 'not' in front of the 'all', to give sentence negation. But no such distinction applies to genuinely singular subjects, i.e. object words. Indeed, he proves this by re-writing the original sentence as "the concept mammal is subordinate to the concept land-dweller". By negating the predicate we get "the concept mammal is not subordinate to the concept land-dweller", which is the contradictory of the original sentence. And so a useful criterion for determining whether an expression is a concept expression (a logical predicate) or an object expression (a logical subject) is to determine whether predicate negation is equivalent to sentence negation or not. If it is, then the grammatical subject is a logical subject as well. Otherwise it is a logical predicate.

With that test in mind, and on the assumption that proper names are logical subjects, direct reference immediately follows, as I shall show tomorrow.

Thursday, May 24, 2012

Frege famously classified the semantic function of a proper name into sense (Sinn) and reference (Bedeutung). But this conceals a difficulty. The sense of a proper name is clearly part of its meaning, and Frege even says this in a letter to Bertrand Russell written in November 1904. My father would have been alive then, although only eight months old. Frege writes

Mont Blanc with its snowfields is not itself a component part of the thought that Mont Blanc is more than 4,000 metres high ... The sense of the word 'Moon' is a component part of the thought that the moon is smaller than the earth. The moon itself (i.e. the Bedeutung of the word 'Moon' is not part of the sense of the word 'Moon'; for then it would also be a component part of a thought. We can nevertheless say: 'The Moon is idential with the heavenly body closest to the earth'. What is identical, however, is not a component part but the Bedeutung of the expression 'the Moon' and 'the heavenly body closest to the earth'. We can say that 3+4 is identical with 8-1; i.e. that the Bedeutung of '3+4' coincides with the Bedeutung of '8-1'. But this Bedeutung, namely the number 7, is not a component part of the sense of '3+4'. The identity is not an identity of sense, nor of part of the sense, but of Bedeutung ...

But if so, in what sense is the 'Bedeutung' a meaning at all? Bedeuten: the German for 'mean' or 'signify'. Frege is clearly disturbed by the idea that Mont Blanc, with its massive snowfields, could be part of a thought. But if it isn't, how could it still be part of the meaning? If Mont Blanc is destroyed in an enormous eruption (here Frege's other analogy to Etna would have been more appropriate), does the meaning of 'Mont Blanc', or some part of it, remain?

And if Mont Blanc itself isn't part of the meaning of its name, there is a further difficulty for Frege's theory that I commented on yesterday. If the name retains its sense after the Bedeutung, the referent, is destroyed, then we must suppose the sense of a name is something permanent to which its referent bears an impermanent and external relation. Let's say the sense is 'satisfied' when the referent exists. So, the sense of 'Mont Blanc' was not satisfied before the enormous geological upheaval created its referent, but is satisfied now, although it would once again not be satisfied if Mont Blanc exploded into nothingness. The difficulty is that his theory depends on the concept-object distinction. According to that distinction, concept words or predicates are fundamentally different from object words or singular terms, in that concept words are sensitive to the scope of negation, whereas singular terms are not. Take 'a man is not running' and 'it is not the case that a man is running'. The predicate negation is true when there is at least one man, and he is not running. The sentential negation is true only when no man runs. But there is no such distinction with singular propositions, at least as the object-concept distinction requires it. 'Socrates is not running' and 'It is not the case that Socrates is running' is true only when Socrates exists, and he is not running. There appears to be no room for the possibility of Socrates not existing. Yet if the meaning of a proper name is its sense, and if the sense exists even when the referent does not, 'Socrates is running' is false when Socrates does not exist, yet 'Socrates is not running' is false as well.

Russell replied, a month later in the days before email, that Mont Blanc really is a part of what is asserted by 'Mont Blanc is more than 4,000 metres high'. I think he changed his mind shortly later, but then Russell often changed his mind (which is a good thing).

As I noted in the page linked above, I could not then find where Russell was writing from. He moved there in 1904 in order to work out a theory of denoting that could be used in Principia Mathematica, but which would avoid the Paradox (now known as Russell's paradox) that he had discovered while working on the Principles of Mathematics. He took his first wife Alys there, but this was a disastrous part of a disastrous marriage, and he was probably not very happy there. Nor actually was she, as Russell seems to have been a beast towards her. Thanks to Google maps I think I have located the place. It certainly is secluded, a short distance from Lower Frensham pond in a fairly exclusive part of the Surrey stockbroker belt. I don't like Surrey. Mostly places like that. Small roads in the English countryside, looking as they might have looked two hundred years ago, then suddenly there appears a large, usually Edwardian mansion at the end of a long gated drive. Inside, they still drink gin and tonic. But nothing wrong with that, I suppose.

Wednesday, May 23, 2012

After reading some of Maverick’s other posts on the subject, and reading some material he sent me, it is clear I have misrepresented his argument. Although I am still some way from understanding it, I think it is this.

Suppose there is only one American philosopher, and suppose that it is Vallicella. Then the sentence ‘an American philosopher exists’ is true because Vallicella (qua American philosopher) exists. Now we can translate ‘an American philosopher exists’ into ‘some philosopher is American’, which reduces the verb ‘exists’ to the copula ‘is’. But we can’t translate ‘Vallicella exists’ in the same way. Thus general existential statements presuppose the truth of singular existential statements (or a disjunction or conjunction of singular existential statements). But we cannot analyse away ‘exists’ from singular existential statements. Therefore there is circularity: the same word appears on the right and left hand side of the definition. An American philosopher exists if and only if Vallicella exists.

But there is an obvious route out of this problem. What actually makes ‘some philosopher is American’ true is ‘Vallicella is an American philosopher’, which does not use the word ‘exist’. Vallicella may object that ‘Vallicella exists’ has to be true for that to work. Certainly, but we can reply in two ways. We could suppose that empty proper names are meaningless, and that ‘Vallicella’ is only meaningful because it names something. I.e. if it names something, it must name an existing something. ‘Vallicella exists’ is therefore true in virtue of the meaning of the proper name ‘Vallicella’. Or we could allow that empty proper names are meaningful, and that they have a sense but not a reference. Then we can appeal to the idea of instantiation, as with general concepts. ‘Vallicella exists’ means that the sense of ‘Vallicella’ has a referent or instance. ‘An American philosopher exists’ means that the sense of ‘American philosopher’ has an instance.

That is, either common names and proper names fall into different logical categories, in which case we don’t need to use the word ‘exists’ in singular sentences at all. Or they fall into the same category, in which case we can analyse singular existential statements exactly as we analyse general existential statements. In neither case is the definition of ‘exists’ circular.

Monday, May 21, 2012

I have expanded the Logic Museum page on 'supposition' to include more about the various divisions of the subject, plus something on 'simple' supposition. I need to write something about 'personal' supposition to complete it, and notice the red link on 'reference'. Reference is a modern notion, no less vague than supposition, and needs careful treatment.

Sunday, May 20, 2012

Jason has questioned which argument of Bill's I am talking about. I did link to one version of the argument (I have been involved with many over the years). But I found another one here, slightly longer. Bill says:

Now either x exists or it does not.

Suppose it does not. Then we have instantiation without existence. If so, then existence cannot be instantiation. For example, let C be the concept winged horse and let x be Pegasus. The latter instantiates the former since Pegasus is a winged horse. But Pegasus does not exist. So existence cannot be the second-level property of instantiation if we allow nonexistent objects to serve as instances of concepts.

Now suppose that x exists. Then the theory is circular: it presupposes and does not eliminate first-level existence. The concept blogging philosopher is instantiated by me, but only because I possess first-level existence. One cannot coherently maintain that my existence consists in my instantiating that concept or any concept for the simple reason that (first-level) existence is what makes it possible for me to instantiate any concept in the first place.

I follow the first leg of the argument. If there are non-existent objects, then existence obviously cannot boil down to instantiation. That is very clear. It is the second leg which makes no sense. The argument seems to be that some philosopher is blogging, only because a blogging philosopher exists. Therefore the existence of a blogging philosopher cannot boil down to some philosopher being a blogger.

One might as well argue that this meat being lamb cannot boil down to this being mutton, for it is lamb because it is mutton. Therefore the definition 'mutton is lamb' is circular. But that argument is blatantly bad.

The verb 'exists' only appears on the left hand side of the definition, and so the definition is not circular, by the definition of circularity. To the objection that the right hand side has an elided adjective 'existing', i.e. that the definition should really be

I appealed to what I will call the 'enlargement principle'. This is the principle that any adjective or qualifying term must, if it is to be meaningful, enlarge the conception signified by the term that it contracts. Thus 'blue' enlarges the concept signified by 'buttercup' when we attach the terms to form the composite 'blue buttercup'. Thus it is meaningful. But 'existing' does not enlarge the concept signified by 'American philosopher', for the sentence 'some philosopher is American' already states that an American philosopher is existing.

Against. Consider the concept signified by 'character in War and Peace'. There are hundreds of such characters. Some of these, such as Napoleon and the Czar of Russia, and the Russian general whose name I have forgotten, are or were historical characters. So they are existent in some sense (i.e. they used to exist, or exist in the afterlife). Others, such as Prince Bolkonsky or Natasha, never existed at all. So the contracting term 'existing' or 'historical' does enlarge the conception signified by the term it is attached to. And it does diminish the extension of the contracted term. The total number of characters in the book is large, but decreases significantly when we consider only the real historical ones. Thus the term 'existing' or 'historical' or 'real' is meaningful, and a real predicate. Thus the thin conception of existence does involve circularity.

Saturday, May 19, 2012

Yesterday’s post caught a few people by surprise. What is the background to all that? What is the ‘thin’ conception of being? Etc. Of course there is a background to this, and it is large, and it should be part of the baggage of anyone studying modern analytic philosophy. So here is a brief history of the subject.

We start in the fourth century B.C. with Aristotle and his Perihermenias, his treatise on the second operation of the understanding, where two simple concepts are combined to form a proposition. In the tenth chapter he has an obscure paragraph about the verb ‘is’ being predicated as a ‘third elements’. In the scholastic Latin which was used to translate Aristotle’s Greek, this is rendered as tertium adiecens, literally third adjoinment or third adjective. What on earth does that mean? Thomas (in the middle of the thirteenth century) makes a valiant attempt to explain it in his commentary on the work. He says that sometimes the verb ‘is’ is predicated by itself in a proposition, such as in “Socrates is“ i.e. Socrates exists. By this we signify that Socrates really exists. That is predication of ‘is’ as a second element, i.e. existence predicated of itself, existence as a predicate. At other times it is not the main predicate but is joined to the main predicate to connect it to the subject, as in “Socrates is white.” Here we are not asserting that Socrates exists, but rather attributing whiteness to him by the verb ‘is’. Hence, ‘is’ said to be a third element, not because it is a third predicate, but because it is a third element or word in the proposition.

Roll forward to the eleventh century and to Anselm and his so-called ontological argument. This was an argument to prove the existence of God through logic alone, by proving that the concept of God has the concept of existence built into it. He argues as follows

… it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction. There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even be conceived not to exist;. and this being thou art, O Lord, our God. (Proslogionchapter 3).

I won’t go into the tortuous logical details of the argument now, but the argument is generally thought to be invalid, and the reason is generally thought to be treating the verb ‘is’ as a predicate, i.e. as the main predicate in the sentence, rather than as a copula or ‘third element’ which simply joins the real predicate (being wise or being good) to the subject.

The whole issue was extensively discussed in the late thirteenth century, but this is rarely if ever mentioned in modern philosophy courses because of the assumption that all philosophy began in the early modern era as a byproduct of the glorious enlightenment process. Thus students tend to hear about the ontological argument in the context of Descartes, rather than Anselm or thirteenth century philosophers. Descartes writes in his Meditation V:

… the existence can no more be separated from the essence of God, than the idea of a mountain from that of a valley, or the equality of its three angles to two right angles, from the essence of a [rectilinear] triangle; so that it is not less impossible to conceive a God, that is, a being supremely perfect, to whom existence is awanting, or who is devoid of a certain perfection, than to conceive a mountain without a valley.

Note that Descartes was writing in Latin, another fact that is sometimes overlooked. This is because we associate the enlightenment process with the modern romance languages rather than Latin, which belongs to the dark ages before the early enlightenment.

Roll forward again to Kant, the glorious eighteenth century philosopher of the high enlightenment, who famously tells us (in The Critique of Pure Reason, A 598/B626) that existence is not a ‘real predicate’. This was a period when all good philosophers wrote in German (Sein* ist offenbar kein reales Praedikat). 'Existence' is not a determining predicate which enlarges the concept of the subject to which it is added, in the way that ‘white’ enlarges the concept ‘man’ by increasing its intension but reducing its extension. When philosophers talk about existence not being a predicate, it is usually Kant’s discussion they have in mind. (Maverick has strong views about this, but I’ll pass over those for now).

Kant had little influence on modern logic, however. The main development of the question whether ‘existence is a predicate’ comes in the middle of the nineteenth century. I have a bit about the history in a discussion of Brentano here, and see also this contemporary paper here. Brentano argued that we can always translate any sentence containing the verb ‘exists’ into one that does not contain it. Thus ‘a sick man exists’ translates to ‘some man is sick’. This idea is the direct ancestor of the modern view, often associates with Quine, that existence is what the existential quantifier expresses. It is uncertain how it got into modern predicate logic, as there are at least three contenders, namely Brentano, Frege and the American Charles Peirce. Probably it was Peirce via the German logician Ernst Schroeder. I wrote a short piece on this for Wikipedia years ago, which is still there (permalink).

So the issue of detail is whether the verb ‘is’ is simply a copula that joins subject to predicate. This is essentially the view embedded into modern predicate calculus and the use of ‘existential’ quantifier. The general and important position that it underlies is whether we can prove the existence of God, or not. If existence is merely ‘someness’, i.e. if ‘existing thing’ is equivalent to ‘something’, the ontological argument does not get off the ground. But if it is something larger or ‘thicker’, the argument at least stands a chance. Thus large things sometimes hang on small things.

One day I should write this history up properly. Every discussion I see has some part of the history, without taking a view of the whole.

*I literally just noticed that Kant is using the German 'sein', which is the infinitive of the German verb 'to be'. English philosophy tends to follow Latin philosophy in using the distinct verbs 'to be' (esse) and 'to exist' (existere). That distinction is a subject in its own right, which I will pass over for now.

Friday, May 18, 2012

For reasons that Bill the Maverick will understand, I have recently been exercised by his argument that the 'thin' definition of existence is circular. He says here, for example, that "to account for the existence of an individual in terms of the instantiation of some concept or property is blatantly circular: if a first-level property is instantiated,then it is instantiated by something that exists" (my emphasis).

The thin conception, as I understand it, is that the first statement below is broadly equivalent to any of the three statements that follow it.

1. An American philosopher exists
2. The concept 'American philosopher' is instantiated
3. There is an American philosopher
4. Some philosopher is American

Maverick, as I understand him, believes that this equivalence involves a circularity. I.e. The definition of the first statement in terms of the second (and probably the third or the fourth, though he has never said this) is circular. What does he mean?

By way of preliminary, let's talk about what a circular definition actually is. A circular definition is one where the left hand term, the term to be defined, the definiendum, contains a term or a word that is also contained in the defining expression, the definiens. For example, if I say, as some people do, that money is whatever people treat as money, that is a circular definition, because the word 'money' is used to define itself. When we look at the right hand of the definition, we have to ask what 'money' means, and so we ask again by putting it on the left, and if we get the same reply, we go on and on in an endless circle.

Now I emphasised 'term' and 'word', because that is very important. The definition is circular because of the repeated word, not because of a repeated concept. Clearly the concepts corresponding to the left and right hand expressions must be repeated, otherwise it wouldn't be a definition. The whole point of a definition is to explain an expression you don't understand in terms of an expression you do understand. For example, you may not understand the word 'mutton', but you may understand the word 'lamb'. So I tell you that mutton is the same thing as lamb, and you understand. Now it's no good objecting that the definition is circular because the concept of mutton presuppposes the concept of lamb, indeed is identical to it. Of course it does, and that is the whole point. I am explaining that the concept corresponding to 'mutton' is identical to the concept corresponding to 'lamb'. So the fact that the same concept occurs (as it were) on both sides of the definition does not mean the definition is circular. On the contrary, that is what makes the definition work in the first place. It's a repeated word that is the only problem.

With that preliminary out of the way, it seems clear that defining (1) above in terms of any of the following three statements is in no way circular. The word 'exists', which is the one we want to explain or define, does not occur in any of the three defining statements. So why does Maverick there is any circularity?

Now he says 'if a first-level property is instantiated, then it is instantiated by something that exists" (my emphasis). That seems to me like objecting that if something is lamb, then it is lamb which is mutton, and so defining mutton as lamb is circular. Which is absurd. Now he may mean that the adjective 'existing' adds something to the expression 'American philosopher', and so 'American philosopher' and 'existing American philosopher' are not equivalent. If that is true, then the definition certainly would be circular. For the statement 'some philosopher is American' of (4) above would be elliptical for 'some philosopher who exists is American', and the defining right hand expression would thus contain the term 'exists', which was on the left hand side. But that is precisely what the thin theorist is denying, indeed strenuously denying. 'Existing philosopher' and 'philosopher' are, for him, exactly the same, and so 'instantiated by something' and 'instantiated by something that exists' are exactly the same, just as 'instantiated by something' and 'instantiated by something that is something' are the same. Indeed, just as 'cooking lamb' and 'cooking lamb which is mutton' are the same.

Or does he mean that the concept of existence is presupposed in statements (2)-(4) above? Well of course it is, just as the concept of mutton is presupposed by the concept of lamb. To understand the statement 'someone is an American philosopher', you have to understand the concept of existence, for the existence of an American philosopher is exactly what the statement asserts. Similarly, in order to understand 'lamb is on the menu' you have to understand the concept of mutton, for the concept of mutton and the concept of lamb are one and the same. But that doesn't mean that the definition 'mutton is lamb' is circular.

Perhaps Maverick intends something different. But if he does, I am very far from understanding it, and the first duty of a philosopher is enable understanding.

Wednesday, May 16, 2012

Phoenician Bill objects to my argument yesterday about singular concepts. Why do we need singular concepts? Why can’t we represent “Vulcan does not exist” as “The concept Small, intra-Mercurial planet whose existence explains the peculiarities of Mercury's orbit is not instantiated”, which involves a general, not a singular, concept?

I reply: see my post last year, also replying to some Phoenician quibble, and in particular the point about the Borgesque thought experiment*. Suppose I write an explicitly fictional story about a planet which I call ‘Vulcan’, unaware of the planet whose real existence was postulated by Verrier. And suppose that in my story Vulcan is a small, intra-Mercurial planet whose existence explains the peculiarities of Mercury's orbit. Then I am not talking about the Vulcan of LeVerrier. Reference to my Vulcan requires acquaintance with my text. Reference to LeVerrier’s Vulcan requires acquaintance with his writing, or writing about his writing which ‘borrows’ the Vulcan reference. As I said:

It is this specific connection to items of information, texts etc. that guarantees the acquisition of individual concepts by different people, and their successful use to make individuating reference. What guarantees that we are thinking about Julius Caesar is the right kind of relation to a certain set of texts – not a relation to any existing person, which is irrelevant. What guarantees that we are all thinking about Frodo is exactly the same kind of relation. The existence of the individual referred to, and even their causal relation to the text, is irrelevant.

This is very important.

*I did not mention it in the post, but I was alluding to Borges story “Pierre Menard, Author of the Quixote”, published in 1939.

Tuesday, May 15, 2012

A proposition has a sense, and the sense of the proposition has a corresponding thought. This is is how we communicate. But we don't attach a simple sign to each thought, otherwise we could only communicate as many thoughts as there were simple signs. So a proposition is composed of simple signs, each of which has a sense. We can put these simple signs together in as many ways as we like, so we can communicate new thoughts.

I do not believe that we can dispense with the sense of a name in logic; for a proposition must have a sense if it is to be useful. But a proposition consists of parts which must somehow contribute to the expression of the sense of the proposition: so they themselves must somehow have a sense. Take the proposition 'Etna is higher than Vesuvius'. This contains the name 'Etna', which occurs also in other propositions, e.g., in the proposition 'Etna is in Sicily'. The possibility of our understanding propositions which we have never heard before rests evidently on this, that we construct the sense of a proposition out of parts that correspond to the words. If we find the same word in two propositions, e.g., 'Etna', then we also recognize something common to the corresponding thoughts, something corresponding to this word. Without this, language in the proper sense would be impossible. We could indeed adopt the convention that certain signs were to express certain thoughts, like railway signals ('The track is clear'); but in this way we would always be restricted to a very narrow area, and we could not form a completely new proposition, one which would be understood by another person even though no special convention had been adopted beforehand for this case.

Monday, May 14, 2012

An excellent post by the Phoenician Maverick on the difficulty of translating 'something exists' into Frege-Russell logic, as defended by Londonista David Brightly.

I don't agree with David 's approach, which is to invent the predicate 'Object(x)', a predicate which is satisfied by everything, and which fails to be satisfied by nothing. This translates 'something exists' into 'for some x, object(x)'. Neat - in Frege-Russell 'for all x F(x)' is true even when nothing exists. But unsatisfying, because there remains the difficulty of negative existential singular sentences. How do we translate 'Pegasus does not exist'? If 'Pegasus' is a name at all, then Object(Pegasus), which translates to 'Pegasus exists', which is false.

I prefer a non-standard logic which (as David knows) extends the Frege approach from general existential statements to singular statements. For Frege, 'serpents exist' means that the concept 'serpent' is instantiated. If we accept singular concepts, it follows that 'Pegasus exists' means that the concept Pegasus is instantiated, and 'something exists' means that some concept is instantiated.

For more on singular concepts, use this search key. Maverick has objected to the notion of singular concepts many times, but has failed to address any of my masterful replies.

Sunday, May 13, 2012

It's Sunday, which is traditionally a time for reflection on higher matters, when the pub plays light jazz on the juke box instead of some awful rap music or death metal, and some folks go to church. So here's Porter Waggoner with some philosophical reflections on Christianity and possibly the hypocrisy of Christian life. I can't decide whether it's awful or not. Did I mention here before that I have a weakness for country music?

Yesterday I discussed arguments for the broadly materialistic principle that "we can characterise thought and understanding entirely without reference to any external object". But let's not confuse that with materialism itself, and certainly let's not confuse it with crude materialism. I am concerned with rejecting the sort of anti-materialist argument that we cannot characterise a thought unless we can specify what it is a thought of, and rejecting an argument against something is obviously not the same as an argument for something.

As for 'crude' materialism, that is a perfect example of the kind of bad, sophomoric philosophy which it is the job of good philosophy to correct. There's a wonderful page full of it here. Someone, probably with an education entirely confined to the hard sciences, has the insight that people are made entirely of atoms. Molecules are made of entirely atoms, ergo humans are molecules. Materialism of the crudest sort. What's wrong with it? Well, I am not sure it is even scientifically correct. Molecules are arrangements of atoms in certain bonding relationships that hold only at the atomic level. So even DNA is not a molecule, but rather a pair of molecules held tightly together. The relationship that ties the heart to liver, and the liver to the brain is not an atomic one. Or is a molecule a set of atoms in any relationship whatsoever? Then a city is a molecule, the Earth and the Sun are molecules, the Earth and the Sun together are a single molecule, the whole universe is a single molecule. That is no help whatsoever.

Even if it is scientifically correct (I'm no expert), how does the insight help? We want to explain the nature of money, for example. Now money is an arrangement of atoms – either atoms of pound notes, or coins, or bond 'paper', or their electronic correlates in the general ledger of a payments system. But how does that help explain money? It is the job of the sciences of economics and finance to do that. How does the science of atoms and thermodynamics help us here? That's not to say that, once we have perfected those sciences, we could give a more complete, but vastly more complicated explanation in terms of atomic theory. My point is that the insight – that things are composed of atoms – does not help us explain economics, aesthetics, history etc.

Sometimes a crude materialism of this sort is used to justify malicious actions. "OK I lied to you, but I am only a collection of atoms, and concepts like good and evil and being 'wrong' are not appropriate to collections of atoms. Therefore what I did was not wrong". Which reminds of the story (I can't remember where I read it), of the man who was about to be executed for murder the next day, and pleaded to the king for clemency. "I could not help my actions, I was determined by my nature and by the stars to commit these evil deed, it was all predestined". To which the king replied "I forgive you. I also forgive the man who is to execute you tomorrow".

Saturday, May 12, 2012

Jason asked if I was holding back whole theories of language, logic, and signification that I had in mind. Well, sort of. I'm one of those people who find blank canvasses intimidating, so I cut them up into tiny squares and fill in each one, day by day, over the years. Obviously this tends to obscure the "big picture".So, here is a brief attempt, before breakfast, to summarise the program I have been working on for some years.

Starting from the top, I suppose my target is the sort of anti-materialist argument that goes roughly as follows. "We cannot characterise a thought properly unless we specify what it is a thought of. But a thought can be of something external to the mind. But brain states are physical states that can be completely characterised without reference to anything external to the mind. Therefore, there can be no adequate explanation of thought in terms of brain states." It sometimes seems to me that the Maverick Philosopher's entire program is devoted to justifying this argument, and my entire program to refuting it. So my entire program is devoting to establishing or giving conclusive evidence for the following, broadly materialist principle.

(1) We can characterise thought and understanding entirely without reference to any external object.

To reduce this large problem to a slghtly smaller one, I make the following assumption:

(2) Significare sequitur intelligere.If we can explain signification without reference to external objects, then likewise we can explain thought and understanding.

I don't have any arguments for this, I simply take it for granted. It was a fundamental principle in medieval philosophy of language, and was also fundamental to the Fregean theory of language that emerged in the early twentieth century (via Russell) and came to dominate analytic philosophy for a long time. Now to establish (1), we need to establish that:

(3) We can explain signification without reference to external objects.

This requires unravelling a set of tightly-knit problems surrounding truth, existence, reference, identity, individuation, and the problem of universals. Roughly, this means establishing the following theses

(4) Reference is not a real relation between a proper name and some object 'referred to'.

What I mean here is that in the sentence "'Socrates' refers to Socrates", the verb phrase 'refers to' is logically intransitive. I.e. it takes a grammatical accusative but not a logical one. The sentence can be true without there being any such thing as Socrates.

(5) Existence is not a property

This is to avoid any unpleasant diversion into a neo-Meinongian theory of reference, according to which we can refer to non-existent objects, and which could be one interpretation of (4) above.

(6) Identity is not a relation

This is to avoid any unpleasant diversion into the sense-reference distinction, and to support the theory of individuation required by (4) above.

(7) The truth conditions of singular sentences can be explained without reference to external objects

This is to sidestep the objection that the meaning of a sentence includes its truth conditions, and the truth conditions of singular sentences cannot be explained without reference to external objects. This is the bit I have been discussing in the most recent set of posts, as well as many earlier ones. I don't believe we can overcome this objection unless we can justify some Ramseyan theory of truth, including the following claim

(8) Assertion is a semantic component of a sentence

I have argued this one repeatedly with the Maverick over the years. I think he dimly sees how it is repugnant to (1). For example, it means rejecting the whole notion of a 'truthmaker', in his sense.

A small prize for anyone who can identify the title of this post. Later, I will pull together some links from 6 years of posts to illustrate the theses above. Now breakfast calls.

Thursday, May 10, 2012

What do the words ‘yes’ and ‘no’ mean? Well, I can explain how their meanings add up. If I add the word ‘yes’ to the question ‘is it raining’ I get something with the same meaning as the assertion ‘it is raining’

“Is it raining? – yes” = ‘it is raining’

Similarly adding the word ‘no’ to the same question gives the corresponding denial:

“Is it raining? – no” = ‘it is not raining’

Does this shed any light on the question about negation and the principles of contradiction and excluded middle? I think so. For I suggested that one who questions either of these principles hasn’t really understood the meaning (or rather, the use) of words like ‘not’. Certainly, one who thinks that both ‘yes’ and ‘no’ are simultaneous replies to the same question, hasn’t understood the meaning of these interjections. For example, suppose someone utters ‘no’ then ‘yes’ in close succession.

“Is it raining? – no… yes” = ‘it is raining’

We would naturally take him or her to have changed their mind. I.e. At the time of uttering ‘no’ they were saying it was not raining, and then retracted it by uttering ‘yes’.

That deals with the principle of contradiction, namely is that it is impossible meaningfully to assert and deny the same thing. As for excluded middle, that follows from the fact that nothing else apart from ‘yes’ and ‘no’ counts as a reply to a question. Note that ‘not sure’ is not a relevant reply, for it is really the reply ‘no’ to the question ‘are you sure that it is raining?’, rather to the question 'is it raining?'. I.e.

"Is it raining? - not sure" = "are you sure it is raining? - no" = "I am not sure it is raining"

Failing to answer is failing to answer. Bullshitting is also failing to answer the question, but by means of asserting all sorts of other irrelevant things, or just outright nonsense.

Wednesday, May 09, 2012

There were (or was?) a flurry of comments on my earlier post about the concept of negation, and the meaning of the word ‘not’. I would say these are quite separate things. Indeed, there are many separate things. Negation is not the same as the concept of negation. For the expression “the concept of negation” is a noun phrase referring to the concept of negation, whereas ‘negation’ refers to negation. As for the word ‘not’, it is an adverb not a noun, and while it clearly has a meaning, it cannot be the same as the meaning of the word ‘negation’. Otherwise we could replace the word ‘negation’ with the word ‘not’ without change of meaning. But ‘snow is not black’ does not mean the same as ‘snow is negation black’. Note also (and I find this a bit puzzling) that the ‘the meaning of the word “not”’ is a noun phrase that refers to the meaning of the word ‘not’. Yet we can’t replace ‘the meaning of the word “not”’ with the word ‘not’ without change of meaning.

There is also the verb ‘negate’. This is derived from the Latin ‘nego’ meaning to deny, and the meaning is still pretty much the same. Negating is denying. This is what the word ‘not’ does when we attach it to a sentence. So the word ‘not’ achieves what the verb ‘deny’ does, and so it has the effect of a verb, yet it is an adverb!

All very confusing. I shall talk about the interjections ‘yes’ and ‘no’ tomorrow.

The Phoenician Maverick helps me out of the mid-week posting famine with this post on whether Wittgenstein was a 'rejectionist' with respect to the question why there is anything at all.

Just a point on the quote: it is Kenny paraphrasing Waismann's note of what Wittgenstein may have said, i.e. it is Wittgenstein's voice here, not Kenny', as Bill seems to suggest in his point #4. Otherwise I agree with him that Wittgenstein's position rests on the saying/showing distinction which is in turn closely connected with the Frege-Russell account of existence. Whether I agree with that position is something which I decline to talk about for the moment. Altissimum enim est huiusmodi negotium et maioris egens inquisitionis.

Monday, May 07, 2012

In judging one judges something; in judging something, one judges something real; so in judging something unreal, one judges nothing; but judging nothing, one is not judging at all.

According to Anscombe* Wittgenstein returned to this problem again and again throughout his life. It presents a formidable challenge to his picture theory of language. He thought, in his early work, that in a proposition we supposedly put together a picture of the world just as in the law-courts of Paris of the early twentieth century, a car accident is represented by means of dolls. So how do we get a picture of negation?

What any picture, of whatever form, must have in common with reality, in order to be able to depict it - correctly or incorrectly - in any way at all, is logical form, i.e. the form of reality. So what reality does a negative proposition represent? What is the reality represented by 'snow is not black'? According to Wittgenstein, the negation operator 'not' does not make a picture at all, but simply performs a truth functional operation on the picture given by the corresponding affirmation. The picture he drew in his early Notebooks (above) shows this clearly**. And in the Tractatus he writes (my emphasis)

4.0621 But it is important that the signs 'p' and '-p' can say the same thing. For it shows that nothing in reality corresponds to the sign '-'.

Determinatio negatio est. Determination is negation. By drawing a circle in the sand we delimit all the sand on the beach outside the circle as well as all which is inside.

Does this help us to understand how the concept of negation is learned? Is negation a concept at all?

*G.E.M. Anscombe, An Introduction to Wittgenstein's Tractatus (London 1971) p.13
**Taken from a nice paper by Robert Pippin here about this subject.

Sunday, May 06, 2012

The Maverick has picked up my post on Siger, which itself picks up an earlier post of his. Is Siger's approach 'rejectionism'? "The rejectionist rejects the question as ill-formed, as senseless." Or is it 'Theologism'? "There is a metaphysically necessary and thus self-explanatory being, God, whose existence and activity explains the existence of everything other than God."

Bill mentions my remark about Wittgenstein, but I can't locate the paper I was thinking of. It was after the Tractatus and either shortly before or shortly after he returned to Cambridge, and it began with the question of why anything exists at all. I can clearly remember looking at it (in Bristol in the early 1980s), but can't locate it.

Meanwhile, I did find an interesting snippet which I quote at second hand from Anthony Kenny's book Wittgenstein. My emphasis:

Logic depends on there being something in existence and there being facts; it is independent of what the facts are, of things being thus and so. That there are facts is not something which can be expressed in a proposition. If one wants to call there being facts a matter of experience, then one can say logic is empirical. But when we say something is empirical we mean that it can be imagined otherwise; in this sense every proposition with sense is a contingent proposition. And in this sense the existence of the world is not an empirical fact, because we cannot think it otherwise (WWK* 77).

Bear in mind that this is Kenny paraphrasing Wittgenstein. But it looks like a genuine form of 'rejectionism' to me. Is it true?

I never thought it possible. A nice shiny new tap. A shame about the fungus bits at the bottom of the tiles. However not all is well. There is still a mysterious damp patch in another part of the kitchen about four feet above ground level, probably caused by demons, as there is no scientific explanation for it.

Saturday, May 05, 2012

The Maverick has been banging on about why there is anything at all, and I have been following it but not commenting (one of those questions that are just too difficult, although that did not stop Wittgenstein having a go*). However I did find something about this by Siger of Brabant**. I give his Latin below, together with my rough translation, made hastily over breakfast. I'm not sure how Siger's reply falls into the categories given by Bill.

For not every being has a cause of its being, nor does every question about being have a cause. For if it is asked why there is something in the natural world rather than nothing, speaking about the world of created things, it can be replied that there is a First immoveable Mover, and a first unchangeable cause. But if it is asked about the whole universe of beings why there is something there rather than nothing, it is not possible to give a cause, for it's the same to ask this as to ask why there is a God or not, and this does not have a cause. Hence not every question has a cause, nor even every being.

*According to Norman Malcolm, Wittgenstein said that he sometimes had a certain experience which could best be described by saying that "when I have it, I wonder at the existence of the world. I am then inclined to use such phrases as 'How extraordinary that anything should exist!'"**Questions on Metaphysics 4 (ed. W. Dunphy, editions de l'Institut superieur de philosophie, Louvain-la-Neuve, 1981 pp. 169-170)

Jason suggested in a comment on the last post that my problem about how we learn to apply negation is related to the ‘Meno question’.

A couple of comments. First, there are two Meno questions or Meno problems. The first is to explain how knowledge is more valuable than mere true belief, and that is the Meno problem as commonly understood. The second problem, which is clearly related to the first, is to explain how we learn anything at all. If knowledge is different from true belief, how can we possibly acquire knowledge by teaching? If teaching is the mere repetition of true propositions (‘The battle of Hastings was in 1066’), and if learning is the acceptance of those propositions as true, on account of the authority of the teacher, or for whatever reason, and if knowledge is more than simple acceptance of the truth, it logically follows that we can’t acquire knowledge from teaching, as so defined. So how do we acquire knowledge? Is it already there, and does teaching in the proper sense require uncovering what lay hidden? – the Latin root of ‘educate’ means ‘drawing out’. Or does it come from without?

The second problem clearly underlies the difficulty about negation, but there is a further difficulty. The medieval philosophers, following Boethius*, divided discourse into three types, namely written, spoken and conceptual. Written discourse signifies spoken discourse, by convention. It is a convention, e.g., that the written word ‘dog’ signifies the noise that comes out of my mouth when I utter ‘dog’. In turn, spoken discourse signifies mental discourse, also by convention. It is by convention that the spoken word ‘dog’ signifies the idea of a dog. French people use the word ‘chien’ to signify that same idea, Germans use the word ‘Hund’ (I think). Ockham, though he was English, would have used the Latin word canis. However, mental discourse signifies not by convention, but ‘naturally’. The English and French and German and Latin words for dog all signify exactly the same thing, namely the idea of a dog. For otherwise we could not communicate, unless we could signify the same idea in another person’s mind as the one we want to convey. But we cannot teach the signification of the idea itself – we don’t have it available to match up with the thing signified, for ideas are private. So ideas or ‘mental terms’ signify naturally. Ockham explains this right at the beginning of his Summa Logicae.

Now the word ‘not’ is what Ockham would have called a syncategorematic term. He explains the distinction in chapter 4, although it does not originate with him. A syncategorematic term is one that does not signify on its own (in the way that the term ‘dog’ on its own signifies or ‘supposits for’ all dogs), but signifies by making other words signify. For example, ‘every’, ‘some’, ‘only’ and of course ‘not’.

If Ockham is right, there is a sense in which we cannot learn the meaning of the word ‘not’. Of course we learn that the English word ‘not’, the spoken word, corresponds to the mental ‘not’, and in that sense we learn the meaning. But in another sense we cannot learn or acquire the mental term itself. It must be already there.

Thus, if he is right, we don’t learn the meaning of negation. It is already there. But is he right?

Friday, May 04, 2012

In learning negation I asked whether we learn the principle of contradiction, and the concept of negation, by observation and experience, or whether it is somehow 'hard wired' into our consciousness. I didn't spell it out, but I was implicitly making two claims. One, that negation is 'hard wired'. Two, that the principle of contradiction follows directly from our concept of negation, i.e. anyone who insists on the possibility that "Socrates is white and Socrates is not white" simply cannot have understood the meaning of 'not'.

Taking the first. It is absurd that the concept of negation is anything we could learn. How, e.g. could you see that something is not white without understanding what negation was, even if you hadn't learned the word 'not' which corresponds to it. Understanding that something is not the case is no less fundamental than understanding that it is the case (presumably those who believe we learn the concept of negation would not defend the learning of affirmation – how would we learn the idea of being the case?). Ergo, the concept of negation is hard-wired.

The second point is harder to prove. I would like to argue that it is a consequence of the position which I have frequently defended here, namely that to assert that p is true is simply to assert p, and that to say that p is false is simply to deny that p. I.e. truth and falsity reduce to affirmation and denial. Does the principle of contradiction follow from this?

Thursday, May 03, 2012

Someone commented (see here and here) about the enigmatic Shepard tone, suggesting it was a case of choosing between the apparently inviolable principle of contradiction, and a phenomenon that apparently contradicted it. I wonder about that.

Look at the Wikipedia definition, which is actually quite good. It says (I paraphrase slightly) it is a tone that continually ascends in pitch, yet which ultimately seems to get no higher. There are two interesting words in that definition, namely 'seems' and 'ultimately', and applying or removing them gives four possible combinations.

(1) The Shepard tone ascends in pitch but does not ascend in pitch

(2) The Shepard tone ascends in pitch but does not seem to ascend in pitch

(3) The Shepard tone ascends in pitch but does not ultimately ascend in pitch

(4) The Shepard tone ascends in pitch but does not ultimately seem to have ascended in pitch

Definition (1) is clearly absurd. A definition needs to give us a way of distinguishing one thing from another, but this gives us nothing, since it includes pitches which do ascend and those which do not ascend, i.e. includes every kind of pitch whatsoever. Definition (2) is better, but is it correct? Surely not. If we take the first two or three tones as they occur in order, they clearly are ascending, and it is not that they just seem to ascend, at least in the initial phases of the sequence. Both definitions (3) and (4) incorporate the term 'ultimately', and here we are getting somewhere. What seems paradoxical about the tone is the way that after a full octave has been ascended, we seem to be back where we were. It's like one of those Sisyphean nightmares where we seem to be climbing forever, and find ourselves back in the same place. Or the Blair Witch Project (for those who remember that).

Yet, in this case at least, is there really any contradiction between appearance and reality? The whole point of the octave interval is the strong resemblance between the two tones of the interval (say, middle C and top C). And where there is resemblance or similarity there is (formal) identity. So it is no paradox to say we are ultimately back in the same place. All the Shepard tone does is to eliminate the respect in which the tones of the interval are different, i.e. eliminates the respect in which C and C' are different, while retaining the similarity.

Why should we find the 'paradox' any more paradoxical than angular movement or modulo change? If you keep on turning around long enough, you will be facing the same direction again. It is midnight, then time passes for each successive hour until it is midnight again. Definition (3) captures the Shepard tone best. It is a tone which ascends in pitch but does not ultimately ascend in pitch, just as an orbit is a movement which changes place but which does not ultimately change in place. What's the problem?
More about the principle of contradiction later.